MinT - Best Known (240−55, 240, s)-Nets in Base 4

Best Known (240−55, 240, s)-Nets in Base 4

(240−55, 240, 1048)-Net over F₄ — Constructive and digital

Digital (185, 240, 1048)-net over F₄, using

trace code for nets [i] based on digital (5, 60, 262)-net over F₂₅₆, using
- net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(240−55, 240, 3340)-Net over F₄ — Digital

Digital (185, 240, 3340)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−55, 240, 777354)-Net in Base 4 — Upper bound on s

There is no (185, 240, 777355)-net in base 4, because

1 times m-reduction [i] would yield (185, 239, 777355)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 780452 787432 636277 899228 951526 501583 146541 754667 818271 634867 706269 345092 963650 717351 169918 428973 028160 038177 644904 334124 798535 494565 081361 055456 > 4²³⁹ [i]